Write the equation of the line passing through the points \( (4,6) \) and \( (-6,-2) \)

To find the equation of the line passing through the points \( (4,6) \) and \( (-6,-2) \), we first calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 6}{-6 - 4} = \frac{-8}{-10} = \frac{4}{5} \] Now, using the point-slope form \( y - y_1 = m(x - x_1) \) with point \( (4,6) \): \[ y - 6 = \frac{4}{5}(x - 4) \] Rearranging it into slope-intercept form, we have: \[ y = \frac{4}{5}x + \frac{14}{5} \] So, the equation of the line is: \[ y = \frac{4}{5}x + \frac{14}{5} \] --- Let’s talk about how the slope of a line affects its steepness! The positive slope of \( \frac{4}{5} \) means that for each 5 units you move horizontally (to the right), you go up 4 units. It’s a great visual to comprehend how lines behave on a graph! Also, cross-checking your calculations is always a good idea. A common mistake is mixing up the points when calculating slope, leading to an incorrect result. Always ensure you've identified \( (x_1, y_1) \) and \( (x_2, y_2) \) correctly to avoid any slip-ups!